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Chapter 13: Problem 31

What is a reradiating surface? What simplifications does a reradiating surface offer in the radiation analysis?

Short Answer

Expert verified
Answer: A reradiating surface is an idealized surface that completely absorbs incident radiation and then re-emits that energy symmetrically. This concept simplifies radiation analysis by assuming conservation of energy, unity emissivity, isotropic angular distribution of emitted radiation, and uniform surface temperature. These assumptions make the calculations involved in radiation analysis more manageable.

Step by step solution

01

Definition of Reradiating Surface

A reradiating surface is an idealized surface that completely absorbs incident radiation and then promptly re-emits that energy in a symmetrical manner. The energy absorbed and emitted by the surface is assumed to achieve a radiative equilibrium, with no net absorption or emission of energy.
02

Simplification 1: Conservation of Energy

With a reradiating surface, energy conservation is easily achieved, as the absorbed energy equals the emitted energy. This simplification allows for easier calculations in radiation analysis as the energy balance at the surface does not change over time.
03

Simplification 2: Surface Emissivity

In reality, surfaces have different emissivities, which quantify their efficiency in emitting radiation. However, with a reradiating surface, it is considered to possess unity emissivity, i.e., an emissivity value of 1. This assumption again simplifies the calculations in radiation analysis since it disregards variations among different surfaces.
04

Simplification 3: Angular Distribution of Emitted Radiation

When considering a reradiating surface, it is assumed that the emitted radiation is uniformly distributed over all angles, leading to a symmetrical and isotropic radiation pattern. This assumption simplifies radiation calculations since the angular components can be factored out, allowing easier computation of radiative transfer between surfaces.
05

Simplification 4: Surface Temperature

For a reradiating surface, the temperature of the surface is considered to be uniform. This assumption simplifies the calculations in radiation analysis because it eliminates the need to consider variations in surface temperature, which can otherwise make the calculations more complex. In conclusion, a reradiating surface is an idealized concept that allows for simplifications in radiation analysis. It assumes conservation of energy, unity emissivity, isotropic angular distribution of emitted radiation, and uniform surface temperature, making the calculations involved in radiation analysis more manageable.

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Most popular questions from this chapter

Two parallel disks of diameter \(D=3 \mathrm{ft}\) separated by \(L=2 \mathrm{ft}\) are located directly on top of each other. The disks are separated by a radiation shield whose emissivity is \(0.15\). Both disks are black and are maintained at temperatures of \(1200 \mathrm{R}\) and \(700 \mathrm{R}\), respectively. The environment that the disks are in can be considered to be a blackbody at \(540 \mathrm{R}\). Determine the net rate of radiation heat transfer through the shield under steady conditions.

An average (1.82 kg or \(4.0 \mathrm{lbm})\) chicken has a basal metabolic rate of \(5.47 \mathrm{~W}\) and an average metabolic rate of \(10.2 \mathrm{~W}(3.78 \mathrm{~W}\) sensible and \(6.42 \mathrm{~W}\) latent) during normal activity. If there are 100 chickens in a breeding room, determine the rate of total heat generation and the rate of moisture production in the room. Take the heat of vaporization of water to be \(2430 \mathrm{~kJ} / \mathrm{kg}\).

Why is the radiation analysis of enclosures that consist of black surfaces relatively easy? How is the rate of radiation heat transfer between two surfaces expressed in this case?

Thermal comfort in a house is strongly affected by the so-called radiation effect, which is due to radiation heat transfer between the person and surrounding surface. A person feels much colder in the morning, for example, because of the lower surface temperature of the walls at that time, although the thermostat setting of the house is fixed. Write an essay on the radiation effect, how it affects human comfort, and how it is accounted for in heating and air-conditioning applications.

Two long parallel 20 -cm-diameter cylinders are located \(30 \mathrm{~cm}\) apart from each other. Both cylinders are black, and are maintained at temperatures \(425 \mathrm{~K}\) and \(275 \mathrm{~K}\). The surroundings can be treated as a blackbody at \(300 \mathrm{~K}\). For a 1 -m-long section of the cylinders, determine the rates of radiation heat transfer between the cylinders and between the hot cylinder and the surroundings.
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